Finite Group Databasebeta

← #16923577

Subgroups — #16923577

Order 4352.

422 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14536730C211yesmaximal, characteristic
2#14530193C212yesmaximal, complemented
3#14526609C212yesmaximal, complemented
4#14526605C211yesmaximal, characteristic
5C17×#2093C211yesmaximal, characteristic
6C2×#10587481—22no—
7#11762748—21no—
8#11762721—22no—
9#11762715C2212yes—
10#11762689—21no—
11#11762684—22no—
12#11762571—22no—
13#11762564C2212yes—
14C2×C17×#107—21no—
15C2×C17×#102—21no—
16C17×#390C2211yescharacteristic
17C17×#384C2211yescharacteristic
18C17×#336C2211yescharacteristic
19C22×D4×C17D411yescharacteristic
20C23×Dic17—21no—
21C22×Dic34D412yes—
22C22×C8×C17—21no—
23C2×C4⋊C4×C17—22no—
24C2×C4⋊C4×C17—21no—
25C2×C4⋊C4×C17D411yescharacteristic
26C2×C22⋊C4×C17—22no—
27C2×C42×C17C2311yescharacteristic
28C2×C22⋊Dic17—21no—
29C2×C22⋊Dic17—22no—
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17D412yes—
32C22×#3622—22no—
33C17×#107—42no—
34C17×#102—42no—
35#10587502—21no—
36#10587502—22no—
37#10587502—22no—
38#10587502—22no—
39#10587481—44no—
40C24×C17—21no—
41C2×D4×C17—21no—
42C2×D4×C17—41no—
43C2×D4×C17—41no—
44C2×D4×C17Q1612yes—
45C22×C4×C17—21no—
46C22×C4×C17—41no—
47C22×C4×C17C2×D412yes—
48C22×C4×C17C2×D411yescharacteristic
49C22×Dic17—22no—
50C22×Dic17—22no—
51C22×Dic17—81no—
52C22×Dic17—82no—
53C2×Dic34—22no—
54C2×Dic34—22no—
55C2×Dic34—42no—
56C2×Dic34—42no—
57C2×C8×C17—22no—
58C2×C8×C17—41no—
59C2×C8×C17—41no—
60C4⋊C4×C17—41no—
61C4⋊C4×C17—41no—
62C4⋊C4×C17—41no—
63C4⋊C4×C17—42no—
64C4⋊C4×C17—42no—
65C22⋊C4×C17—42no—
66C22⋊C4×C17—42no—
67C42×C17—41no—
68C22⋊Dic17—82no—
69C22⋊Dic17—81no—
70C4⋊Dic17—42no—
71C4⋊Dic17—81no—
72C2×#3622—42no—
73C2×#3622—42no—
74C2×#3622—42no—
75#7821—171nomaximal, Sylow
76C23×C17—22no—
77C23×C17—42no—
78C23×C17—41no—
79C23×C17—42no—
80C23×C17—41no—
81C23×C17#12011yescharacteristic
82D4×C17—42no—
83D4×C17—81no—
84C2×C4×C17—21no—
85C2×C4×C17—22no—
86C2×C4×C17—21no—
87C2×C4×C17—22no—
88C2×C4×C17—42no—
89C2×C4×C17—41no—
90C2×C4×C17—82no—
91C2×C4×C17—81no—
92C2×C4×C17C2×Q1611yescharacteristic
93C2×C4×C17#13512yes—
94C2×C4×C17AGL(1,ℤ/8)12yes—
95C2×C4×C17#13711yescharacteristic
96C2×Dic17—42no—
97C2×Dic17—42no—
98C2×Dic17—42no—
99C2×Dic17—42no—
100C2×Dic17—42no—
101C2×Dic17—42no—
102C2×Dic17—84no—
103Dic34—44no—
104Dic34—82no—
105C8×C17—42no—
106#3622—82no—
107#2804—171no—
108#2093D1711yescharacteristic
109#2072—172no—
110#1272—172no—
111#1270—171no—
112C22×C17—42no—
113C22×C17—44no—
114C22×C17—82no—
115C22×C17—81no—
116C22×C17—81no—
117C22×C17#44912yes—
118C22×C17#45111yescharacteristic
119C22×C17#45311yescharacteristic
120C22×C17#45512yes—
121C22×C17#45811yescharacteristic
122C4×C17—22no—
123C4×C17—22no—
124C4×C17—21no—
125C4×C17—21no—
126C4×C17—81no—
127C4×C17—161no—
128Dic17—82no—
129Dic17—82no—
130C2×#107—21no—
131C2×#103—342no—
132C2×#102—21no—
133#400—341no—
134#393—342no—
135#391—172no—
136#390C2×D1711yescharacteristic
137#386—341no—
138#385—342no—
139#384C2×D1711yescharacteristic
140#340—342no—
141#336—172no—
142#336C2×D1711yescharacteristic
143C2×C17—82no—
144C2×C17#161212yes—
145C2×C17#161411yescharacteristic
146C2×C17#162011yescharacteristic
147C2×C17#164412yes—
148C2×C17#165911yescharacteristic
149C22×Q8—172no—
150C22×D4C22⋊D1711yescharacteristic
151C23×C4—341no—
152C22×C8—21no—
153C22×C8—342no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—172no—
157C2×C4⋊C4—341no—
158C2×C4⋊C4C22⋊D1711yescharacteristic
159C2×C22⋊C4—22no—
160C2×C22⋊C4—342no—
161C2×C22⋊C4—341no—
162C2×C42C22×D1711yescharacteristic
163#107—42no—
164#103—684no—
165#102—42no—
166#95—342no—
167#95—341no—
168#95—342no—
169#95—342no—
170C17#782111yescharacteristic, complemented, Sylow
171C24—21no—
172C2×Q8—342no—
173C2×Q8—342no—
174C2×Q8—682no—
175C2×Q8—682no—
176C2×D4—21no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4#6323112yes—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—342no—
183C22×C4—342no—
184C22×C4—1361no—
185C22×C4—1362no—
186C22×C4D4×D1712yes—
187C22×C4C2×C22⋊D1711yescharacteristic
188C2×C8—22no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—682no—
192C2×C8—682no—
193C2×C8—682no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—682no—
200C4⋊C4—1361no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C22⋊C4—1362no—
204C22⋊C4—1361no—
205C42—41no—
206C23—22no—
207C23—42no—
208C23—41no—
209C23—42no—
210C23—41no—
211C23#1058762311yescharacteristic
212Q8—684no—
213Q8—1362no—
214D4—42no—
215D4—81no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—82no—
223C2×C4—81no—
224C2×C4—682no—
225C2×C4—682no—
226C2×C4—682no—
227C2×C4—682no—
228C2×C4—682no—
229C2×C4—682no—
230C2×C4—1364no—
231C2×C4#1058759712yes—
232C2×C4#1058759812yes—
233C2×C4C2×#6323111yescharacteristic
234C2×C4#1058763711yescharacteristic
235C8—42no—
236C8—1362no—
237C22—42no—
238C22—44no—
239C22—82no—
240C22—81no—
241C22—81no—
242C22#1176295112yes—
243C22#1176296411yescharacteristic
244C22#1176297611yescharacteristic
245C22#1176298512yes—
246C22#1176299811yescharacteristic
247C4—22no—
248C4—22no—
249C4—21no—
250C4—21no—
251C4—81no—
252C4—161no—
253C4—1362no—
254C4—1362no—
255C2—82no—
256C2#1452779512yes—
257C2#1452780811yescharacteristic
258C2#1452784111yescharacteristic
259C2#1452799712yes—
260C2#1452808811yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#2093C2
socleC23×C17#120
prime radicalC22×D4×C17D4
hypercenter#2093D17
hypocenterC17#7821
LCSG ▷ C2×C42×C17 ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2093

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14530193C2semidirect
3. #14526609C2semidirect
170. C17#7821semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145367302
#145301932
#145266092
#145266052
C17×#20932
#782117